During the song "How do You Solve a Problem like Maria" one of the nuns says that Maria wears curlers underneath her wimple. The wimple is the white thing the nuns wear underneath the black veil, and it appears that as a postulant (novice?), Maria never wears one. I can understand this though, since "veil" wouldn't really fit into the lyrics.

A wimple is a head covering used by nuns under their veils. A wimple is also a sleeping cap that a nun uses while in bed. Postulants, Novices, along with All nuns (simple and solumn professed) wears a wimple in bed. Novices, Simple and Solumn professed wore an outer wimple under their veils.
If you saw the movie "Song of Bernadette" the cap she wore on her deathbed was a wimple. Or if you saw the movie, "The Nun Story" Sister Luke was recovering from TB in the Congo, while in bed, she had a wimple on.

A postulant would not wear a wimple--but she would wear a cap, a snug white headcovering to which to pin the veil. In the opening scene, when Maria grabs the veil from the ground and runs back to the Abbey, you can see the white border against the black veil--and, I think, the cap as well. In those days, these probably were tied in back (under the veil) to make them fit more closely. Many traditional Orders still wear a cap and/or wimple under the veil.

The wimple has three forms - either as a circle with a hole for the face, as a hood form with a band that sits tight to the face, or as a tube that is wide at the shoulders and narrow at the end you put over your face. If there is a lot of fabric below the chin, the third form was used, if the wimple seems smooth with little extra fabric, then the hood form was used, if the hood seems draped on all sides with vertical folds hanging down, it is the circle form.